Spatial Imputation

This method imputes missing gene expression by borrowing information from spatially proximal cells or spots. It operates on the principle of Tobler's First Law of Geography—nearby locations are more similar than distant ones.

• Weighted Averaging: Uses distance-decay functions to give higher weight to immediate neighbors.
• k-Nearest Neighbors (kNN): Restricts the borrowing pool to the k most similar spatial locations.
• Application: Effective for smoothing technical noise in low-resolution platforms like Visium.

Deep learning models that treat spatial spots as nodes and physical proximity as edges in a graph. They learn latent representations that respect tissue architecture to predict missing gene values.

• Message Passing: Nodes aggregate information from their connected neighbors iteratively.
• Context-Aware: Unlike simple smoothing, GNNs learn complex, non-linear spatial dependencies.
• Example: Architectures like Graph Attention Networks (GATs) assign varying importance to different neighbors, mimicking cell-cell communication logic.

Leverages co-expression patterns from external reference datasets (e.g., single-cell RNA-seq atlases) to infer the expression of unmeasured genes in a spatial context.

• Cross-Modality Mapping: Transfers rich gene profiles from dissociated single-cell data onto tissue maps.
• Probabilistic Models: Uses Bayesian frameworks to estimate the likelihood of a gene being expressed based on the observed expression of its correlated partners.
• Key Tool: Tangram and SpaGE align spatial and single-cell data manifolds to fill in missing transcriptomic gaps.

Uses Generative Adversarial Networks (GANs) or Diffusion Models to computationally enhance spatial resolution, predicting single-cell or sub-cellular expression from multi-cellular spot data.

• Hallucination Control: Trained to generate high-resolution maps that are statistically indistinguishable from real high-resolution data.
• Histology-Guided: Often conditions the generation process on the underlying tissue histology image to ensure anatomical plausibility.
• Example: XFuse and iStar algorithms infer fine-grained expression patterns by integrating pixel-level visual features with spot-level transcriptomics.

Decomposes the sparse gene expression matrix into lower-dimensional latent factors while imposing spatial smoothness constraints on the factor loadings.

• Regularization: Adds a penalty term that encourages neighboring locations to have similar latent representations.
• Denoising: Separates true biological signal from technical spatial dropout events.
• Method: SpatialPCA and NMF variants incorporate spatial kernels to ensure that the inferred factors map to contiguous tissue domains.

A mathematical framework that finds the most efficient way to map the distribution of cells from a reference scRNA-seq dataset onto spatial coordinates, effectively imputing missing genes.

• Wasserstein Distance: Minimizes the 'cost' of moving gene expression mass between the reference and spatial datasets.
• Unified Reconstruction: Reconstructs a full transcriptome-wide spatial map by aligning the two modalities.
• Key Tool: novoSpaRc and CytoSpace use optimal transport to probabilistically assign single-cell profiles to tissue locations, filling in unmeasured transcripts.